Problem 39 - College Algebra Essentials

Question

Evaluate each expression without using a calculator. $$\log _{5} 5^{7}$$

Step-by-Step Solution

Answer

The simplified answer to the problem \( \log _{5} 5^{7} \) is 7.

Step 1: Understand the logarithm property

The property of logarithms to find is; if you take a logarithm of a base to that same base, it's 1. For instance, \( \log _{x} x^{y} = y \). Here, x is the base and y is the exponent.

Step 2: Apply the logarithm property to the problem

Apply the log property to the expression \( \log _{5} 5^{7} \), the log base 5 of 5 to the 7 power, and it will be equal to 7.